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/* Single-precision floating point e^x.
Copyright (C) 1997-2013 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Geoffrey Keating <geoffk@ozemail.com.au>
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<http://www.gnu.org/licenses/>. */
/* How this works:
The input value, x, is written as
x = n * ln(2) + t/512 + delta[t] + x;
where:
- n is an integer, 127 >= n >= -150;
- t is an integer, 177 >= t >= -177
- delta is based on a table entry, delta[t] < 2^-28
- x is whatever is left, |x| < 2^-10
Then e^x is approximated as
e^x = 2^n ( e^(t/512 + delta[t])
+ ( e^(t/512 + delta[t])
* ( p(x + delta[t] + n * ln(2)) - delta ) ) )
where
- p(x) is a polynomial approximating e(x)-1;
- e^(t/512 + delta[t]) is obtained from a table.
The table used is the same one as for the double precision version;
since we have the table, we might as well use it.
It turns out to be faster to do calculations in double precision than
to perform an 'accurate table method' expf, because of the range reduction
overhead (compare exp2f).
*/
#include <float.h>
#include <ieee754.h>
#include <math.h>
#include <fenv.h>
#include <inttypes.h>
#include <math_private.h>
extern const float __exp_deltatable[178];
extern const double __exp_atable[355] /* __attribute__((mode(DF))) */;
static const float TWOM100 = 7.88860905e-31;
static const float TWO127 = 1.7014118346e+38;
float
__ieee754_expf (float x)
{
static const float himark = 88.72283935546875;
static const float lomark = -103.972084045410;
/* Check for usual case. */
if (isless (x, himark) && isgreater (x, lomark))
{
static const float THREEp42 = 13194139533312.0;
static const float THREEp22 = 12582912.0;
/* 1/ln(2). */
#undef M_1_LN2
static const float M_1_LN2 = 1.44269502163f;
/* ln(2) */
#undef M_LN2
static const double M_LN2 = .6931471805599452862;
int tval;
double x22, t, result, dx;
float n, delta;
union ieee754_double ex2_u;
{
SET_RESTORE_ROUND_NOEXF (FE_TONEAREST);
/* Calculate n. */
n = x * M_1_LN2 + THREEp22;
n -= THREEp22;
dx = x - n*M_LN2;
/* Calculate t/512. */
t = dx + THREEp42;
t -= THREEp42;
dx -= t;
/* Compute tval = t. */
tval = (int) (t * 512.0);
if (t >= 0)
delta = - __exp_deltatable[tval];
else
delta = __exp_deltatable[-tval];
/* Compute ex2 = 2^n e^(t/512+delta[t]). */
ex2_u.d = __exp_atable[tval+177];
ex2_u.ieee.exponent += (int) n;
/* Approximate e^(dx+delta) - 1, using a second-degree polynomial,
with maximum error in [-2^-10-2^-28,2^-10+2^-28]
less than 5e-11. */
x22 = (0.5000000496709180453 * dx + 1.0000001192102037084) * dx + delta;
}
/* Return result. */
result = x22 * ex2_u.d + ex2_u.d;
return (float) result;
}
/* Exceptional cases: */
else if (isless (x, himark))
{
if (__isinff (x))
/* e^-inf == 0, with no error. */
return 0;
else
/* Underflow */
return TWOM100 * TWOM100;
}
else
/* Return x, if x is a NaN or Inf; or overflow, otherwise. */
return TWO127*x;
}
strong_alias (__ieee754_expf, __expf_finite)
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